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On the Oriain of the " 4686 " Series. 

By Thomas E. Mebton, B.Sc. (Oxon.), Lecturer in Spectroscopy at University 

of London, King*s College. 

(Communicated by A. Fowler, F.R.S. Eeceived March 25, 1915.) 

[Plate 3.] 

In recent years the class of spectrum lines known generally as the enhanced 
lines has become of especial importance in connection with their bearing on 
modern views as to the constitution of the atom. These lines were first 
investigated by Sir J. IsT. Lockyer, whose classical researches in this field have 
shown that a high order of energy is required for their production, and that 
they are especially conspicuous in many stellar spectra. 

An important paper has recently been published by Fowler,* who has shown 
that the enhanced lines of the elements of the alkaline earth group can be 
arranged in series similar to those obtained in arc spectra, but that for these 
series Eydberg's constant N has to be replaced by the value 4:1^. 

In 1896, Pickeringf discovered in the spectrum of the star ^ Puppis a series 
of lines, which from their numerical relationship to the Balmer series were 
attributed to hydrogen, and which were considered by Eydberg| to be the 
Sharp series of hydrogen, the Balmer series being regarded as the Diffuse 
series. From the f Puppis series, Rydberg calculated the Principal series, the 
first line of which should have a wave-length of 4688 A.U., and his conclusions 
were supported by the fact that a very strong line of about this wave-length 
was found to occur in the spectra of the nebulae and certain stars. 

Fowler| subsequently observed the ^Puppis series, and also a series the 
first member of which had a wave-length of 4686 1..U., in vacuum tubes- 
containing helium and hydrogen, which were excited by a strongly condensed 
electric discharge. Another series was also observed, the first member of 


which was at X == 3203 A.U., and which converged to the same limit as the 
4686 series, being apjDarently a second Principal series. The three series were 
approximately represented by the formulae 

^ ' Phil. Trans./ A, vol. 214, p. 225 (1914) 

t * Astrophys. Journ.,' vol. 4, p. 369 (1896) ; vol. 5, p. 92 (1897), 

I 'Astrophys. Journ.,' vol. 7, p. 233 (1899). 

§ ' Monthly Notices, RA.S.,' December, 1912. 

On the Origin of the " 4686 " Series, 383 

t Puppis series ?i = N -| -5 — ^ — — 77-^7^ r > 7?z = 2, 3, 4 ... 

First Principal series n = N -I t-i^— 7 :rro r > m = 1, 2, 3 ... 

Ll'5^ (m + 1) J 

Second Principal series ^i = X J -—0—7 tttt^ > , m = 2, 3, 4 ... 

^ 11*5^ (m + 0-5)2 J 

Fowler was unable to obtain these lines from hydrogen in the absence of 
helium, but the theoretical investigations of Eydberg appeared to justify the 
conclusion that the series in question were due to hydrogen. 

Bohr* has developed a theory, involving the use of Planck's quantum 
hypothesis, by which he has arrived at formulae for the series of lines emitted 
by an atom of the type investigated by Sir E. Eutherford.f On the 
assumption that the hydrogen atom consists of a central positive nucleus 
with a single electron moving around it, Bohr arrived at a formula which 
closely represented the Balmer series. Assuming further that the helium 
atom consists of a central positive nucleus with two electrons around it, Bohr 
found that the formulae obtained closely represented the 4686 and associated 
series, and by introducing a small correction for the mass of the nucleus, 
the numerical agreement obtained was remarkably close. Bohr accordingly 
suggested that the lines in question were due to helium. According to Bohr's 
theory, the 4686 and 3203 series can be united into one, having a constant 4F 
instead of N", the correction for the mass of the nucleus involving a modified 
value of K, and the ^ Puppis lines being alternate members of a 4ISr series. 

The theory has given rise to a considerable amount of theoretical discussion, 
into which it is not proposed to enter, but it involves the following assumption, 
with which the present investigation is concerned, namely, that the 4686 and 
f Puppis series owe their origin to helium, and are produced during the 
binding of an electron by a helium atom, from which two electrons have been 
removed by the exciting source. 

FowlerJ has come to the conclusion that the series in question are due to 
helium, from analogy with the 4N series of the alkaline earth metals, and 
has pointed out that the enhanced lines in general may possibly be explained 
in this manner, the arc lines being due to the binding of an electron by an 
atom from which only one electron has been removed. 

This view constitutes a wide departure from the earlier hypothesis of the 
proto-elements, whose mass would probably be some simple fraction of the 

^ ' Phil. Mag.,' vol. 26, pp. 1, 476, and 857 (1913) ; vol. 97, p. 506 (1914). 
•t 'Phil. Mag.,' vol. 21, p. 669 (1911). 
J Loc. ctt.y *Phil. Trans.^ 

384 Mr. T. R Merton. 

parent atom, whilst the removal of two electrons from an atom would not 
appreciably affect the mass. 

With regard to the origin of the lines, the spectroscopic evidence certainly 
points to helium. Evans* has observed the 4686 and associated series in 
vacuum tubes from which the hydrogen had apparently been completely 
eliminated, and Starkf has also observed the 4686 line in a helium tube 
showing no trace of the hydrogen lines. This evidence, however, is not 
conclusive. The extreme difficulty of preparing vacuum tubes free from 
hydrogen is well known, and the absence of hydrogen lines from the 
spectrum cannot be taken as conclusive evidence that hydrogen is not 
present. It is true that 4686 has not been observed in vacuum tubes 
containing pure hydrogen, but the same may be said of ultra-violet members 
of the Balmer series, which only appear in hydrogen tubes when helium is 
also present.! In the present investigation an attempt has been made to 
obtain some evidence of the nature of the atoms concerned in the production 
of the 4686 series. 

The method adopted has been a determination of the highest order of 
interference of the spectrum lines at which the fringes, produced by the 
method of Fabry and Perot, remain visible. This depends on the widths of 
the spectrum lines, a problem which was first treated by Lord Eayleigh,§ 
and which has been the subject of quantitative investigation by Michelson.|| 
The whole problem has recently been discussed by Lord Eayleigh.lT It has 
been shown that the chief cause which determines the breadth of a spectrum 
line, produced in a gas at low pressure, is the Doppler effect due to the 
motions of the luminous particles in the line of sight. The limiting order of 
interference at which fringes may still be visible is given by the relation 

N = Kv/(M/T), 

where IST is the limiting order of interference, K a constant, M the atomic 
weight of the luminous particle, and T the absolute temperature. The 
validity of this formula has been experimentally proved by Buisson and 

If therefore a source of light, e.g. a vacuum tube, emits a radiation from an 
atom whose mass is known, it is possible to calculate the mass of an atom 

* * Nature,' vol. 92, p. 5 ; * Phil. Mag.,' vol. 170, p. 284 (1915). 
+ ' Yerh. d. Deutscli. Phys. Ges.,' vol. 16, p. 468 (1914). 
X Cf. Liveing and Dewar, ' Koy. Soc. Proc.,' vol. 67, p. 467 (1900). 
§ ' Phil. Mag.,' vol. 27, p. 298 (1889). 

II 'Phil. Mag.,' vol. 34, p.,280 (1892) ; ' Astrophys. Journ.,' vol. 3, p. 251 (1896). 
^ ' Phil. Mag.,' vol. 170, p. 274 (1915). 
^^ ' Journ. de Physique,' vol. 2, p. 442 (1912). 

On the Origin of the " 4686" Series. 385 

emitting another radiation, from a determination of the limiting orders at 
which these two radiations show interference fringes. The exact value of 
the constant K and the temperature T need not be considered. This 
method of determining the mass of an atom from the breadth of the 
spectrum lines has recently been applied by Buisson, Fabry, and Bourget* 
in their remarkable investigation of the Orion nebula. The validity of the 
formula is restricted to cases in which the radiations are produced in gases 
at low pressures, since, at higher pressures, broadening of the lines is also 
caused by disturbances depending on collisions between the luminous 
particles. Michelson {loc, cit.) has investigated the effect of pressure on the 
breadth of the lines, and his results show that at pressures as low as 
one-thousandth of an atmosphere the effect of collisions may be entirely 
neglected, and at a pressure of 5 mm. of mercury, the broadening due to this 
cause is still extremely small. 

A vacuum tube containing helium and hydrogen at low pressure was 
excited by an induction coil, with a capacity of 0'002o microfarad and a spark- 
gap in the circuit, the spectrum thus obtained consisting of helium lines, 
hydrogen lines, and 4686. 

The pressure in the tube was very low, so that the glass walls fluoresced, 
the 4686 line appearing only outside the capillary, in accordance with the 
observations of Fowler.f A convergent beam of light from the vacuum tube 
was thrown by means of a lens on to the plates of a Fabry and Perot sliding 
interferometer, and the ring system was focussed by means of an achromatic 
lens on to the slit of the spectograph, which consisted of a large Hilger 
constant deviation spectroscope provided with a camera attachment. With 
this instrument a series of photographs could be taken on the same plate. 
The experiments were conducted as follows : — 

The interferometer plates were set at a small difference of path and a 
photograph was taken. The difference of path was then successively 
increased and a series of exposures was made. From the series of photo- 
graphs thus obtained the limiting order could be estimated. In estimating 
the limiting order, it will be seen that since on each exposure the order 
number increases with decreasing wave-length, it is usually possible (if the 
differences of path have been suitably chosen) to pick out some line in which 
the fringes are just visible. The determination cannot be made with a high 
degree of accuracy, but all the photographs taken have yielded concordant 

In Plate 3, I shows a photograph taken through an etalon giving a 

^ ' Astropliys. Journ.,' vol. 3, p. 256 (1914). 
t Zoc. ciV., '^ Monthly Notices.' 

VOL. XOI. — ^A. 2 H 

386 Mr. T. R Merton. 

difference of path of 13 mm. It will be seen that the helium lines show 
sharp rings, whilst the 4686 line and the hydrogen Mnes show no trace of 
interference. The plates of this etalon were more heavily silvered than the 
plates of the interferometer, the fringes being, in consequence, more sharply 
defined. II shows a series of photographs taken with the interferometer, 
the differences of path being %, 4, 12, 16, 20, and 24 mm. The lines at 4471, 
4026, and 3889 are much over-exposed, and the fringes are consequently very 
indistinct. The limits of interference cannot be seen in the reproductioii, 
but on the original plate fringes were just visible in 4686 at A = 4 mm., and 
in helium (X = 4388) at 24 mm. (The hydrogen lines are not visible on this 

This gives 

4686 = r^ t\,^i^,nc^f. ^^Cl IN He = 

0-0004686 "' 0-0004388' 

and for the mass of the system from which 4686 originates (He = 4), 

. / 4 X 0-0004388 Y _ 

^ ^ Ux 0-0004686 == ^^^"^ ^-^^^^ 

or about one-tenth of the mass of the hydrogen atom. 

It has been pointed out by Lord Eayleigh (foe. dt.) that Miohelson's 
assumption that the temperature of the gas in an electrically excited vacuum 
tube is not very different from that of the walls of the tube has been amply 
confirmed by Buisson and Fabry {loo. cit.) in their determination of the change 
in the value of N" when a discharge tube is immersed in liquid air. I have 
noticed, however, that in the case of the ordinary helium lines the value of IST 
becomes smaller when capacity and a spark-gap are mtroduced, keeping the 
current through the primary of the coil unaltered. Buisson and Fabry 
(loc, cit) state that under similar conditions broadening occurs in the lines of 
the Balmer series, but not in the lines of the secondary hydrogen spectrum, 
and they point out that this would indicate some special cause of broadening 
for the Balmer series. ISTo. mention is made of the pressure in the vacuum 
tubes at which this observation, was made, and at low pressures even a feebly 
condensed discharge, extinguishes the secondary spectrum. 

Very little is known with regard to the origin of the secondary spectrum, 
and the broadening of the Balmer series and of the helium lines may possibly 
be explained as being due to the sudden rise of temperature at each, impulse, 
but the above calculation might, by analogy, have no significance if the 
ordinary helium lines corresponded to the secondary hydrogen spectrum. 
This appears to be unlikely for several reasons. In particular, the solar 
chromosphere shows tlie Balmer series and the ordinary helium lines very 


Roy. Soc, Proc, A, VoL 91 PL 3. 







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On the Origin of the '' 4686 '' Series. 387 

strongly, but contains no trace of the secondary hydrogen spectrum. This 
would indicate that the ordinary helium spectrum and the Balmer series were 
analogous. On the other hand, however, in such experiments as those of 
King* the Balmer series behave as enhanced lines, a supposition apparently 
negatived by Fowler's {loc. cit.) demonstration that the Eydberg constant of 
enhanced series is 4N" instead of N*. 

In any case the observed broadening with a condensed discharge would by 
itself appear to limit the use of the method employed to cases in which the 
radiations are produced simultaneously. Thus, in the case of argon, values 
of N" have been found to vary in the red and blue spectra in the ratio of 
7*5 to 1, but for the reason given above it is impossible to attach any 
quantitative meaning to the result. However, in the observations of 4686 
and helium the spectra are produced simultaneously. It is possible that this 
method of calculating the mass of the luminous particles may not be 
applicable to the enhanced lines, the breadth of which may be controlled by 
circumstances at present unknown, but if the method is valid in such cases, 
the results would indicate that the 4686 line is due to systems of subatomic 

"^ ' Astrophys. Journ.,' vol. 38, p. 315 (1913). 

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C^ CO 

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